Sparsity penalized mean–variance portfolio selection: analysis and computation

We consider the problem of mean–variance portfolio selection regularized with an \(\ell _0\) ${\ell }_0$ -penalty term to control the sparsity of the portfolio. We analyze the structure of local and global minimizers and use our results in the design of a Branch-and-Bound algorithm coupled with an advanced start heuristic. Extensive computational results with real data as well as comparisons with an off-the-shelf and state-of-the-art (MIQP) solver are reported.